Yeshiva A or Bais Yaakov A has serious financial problems. They are doing all they can to stay viable, however unless a big donor steps forward they will be forced to close. If the school tells the parents how critical the situation is, that alone will make the parents look for other schools, and by the additional loss of tuition the school will for sure close. Yet if they do not tell the parents the situation and continue to try to find the big donor they need, they may be forced to close right before school starts and thus the parents may be stuck without a school for their children. What is the responsibility of the school towards the parents Halachically? How open do they have to be with the financial situation they are in?
The Torah says, "Do not place a stumbling block before the blind." It also commands to distance oneself from falsehood. It sounds like in your scenario, the parents have an understanding that the ability for their children to go to the school is secure, and they are trusting that there isn't a doubt about that by virtue of not looking to put their kids into alternative schools. By withholding the truth, you are implicitly letting the parents believe there is a school they can go to, and you are preventing the parents from having the information they need to make the decisions for their children.
Imagine a businessman trying to get investors into his business. And they initially are willing to invest because it seems like there will be a larger investor to make the business secure. If the businessman finds out the big investor might not end up investing, and he withholds this information from the smaller investors, he may cause them to lose their money that they may not be able to afford to risk. It would be dishonest and wrong.
In my opinion, you would be required to be honest about the situation before the parents lose the opportunity to put their kids into a different school.
if a parent asks the school for advice then as the Mesilat Yesharim writes in ch.11
The obligation of the upright man when someone comes to him for advice is to counsel him what he himself would have done in a similar situation, without looking at any purpose whatsoever, distant or immediate, other than the benefit of the person asking advice.
Rabbi Avraham Erlinger, a yeshiva Rabbi in Kol Torah, Jerusaelm comments there:
It is common among sellers of merchandise, or shadchanim (matchmakers) or anyone who has a yeshiva and seeks talmidim (students)... in all these things there is a great trial (nisayon) for one who has personal interests to advise according to what is good for himself and his relatives and students... even if his advice is good for the public, and there is a Kidush Hashem (sanctification of God's Name), or kindness to the public - all this is not a permit against this mitzva of "do not put a stumbling block before the blind", whose obligation is to give a beneficial and suitable advice according to the questioner.
and even if the parents are ignorant of the situation, then I think the words later on of the Mesilat Yesharim apply:
The Branches of the sin of "profanation of [God's] Name" (Chillul Hashem) are also numerous and great. For a person must be exceedingly concerned of his Master's honor. In everything he does, he must look and contemplate exceedingly that there will not come out of this something which may cause a profanation of the honor of Heaven, God forbid.
Rabbi Erlinger comments there:
ER - "which may cause" - hence not only actively profaning God's Name is forbidden but even causing this indirectly (grama), or doubly indirectly (grama d'grama). Namely, that one's deeds should not lead to a profanation of the honor of Heaven... We also learn here, that even when there is a doubt that one's deeds may lead to a profanation, this is also sufficient [to forbid] as can be seen from the examples given by Rabeinu which are just concerns that perhaps people will say he did not act befittingly...